Static Analysis of Functionally Graded Sandwich Plates under Normal Environment Using a New Discrete Kirchhoff Quadrilateral Element

In this work, a modified four-node discrete Kirchhoff quadrilateral element is introduced, integrating 3rd-order shear deformation theory to investigate the static response of Functionally Graded (FG) sandwich plates under a steady thermal environment. Each node includes seven degrees of freedom- comprising 3 translations, 2 rotations, and 2 mid-surface shear strains. To eliminate the requirement for C1 continuity in deflection interpolation under the 3rd-order framework, a refined Kirchhoff constraint technique is utilized. Originally formulated for isotropic thin Kirchhoff plates, this approach is now extended to accommodate shear-deformable FG structures. The gradation of material properties across the plate thickness is captured using the rule of mixtures. FG sandwich plates with varying thickness distributions are subjected to sinusoidal loads to assess both deflection and stress characteristics. The outcomes are expressed in non-dimensional forms of stress and displacement. A corresponding finite element formulation and computational code are developed to study simply supported and clamped boundary conditions. The obtained numerical results are validated against established analytical solutions available for both 2-dimensional and 3-dimensional models. The study confirms that the proposed quadrilateral element offers superior accuracy and efficiency compared to other 3rd-order theory-based elements. Moreover, the model proficiently characterizes the distribution of transverse shear stresses. Major Findings: A novel 4-node discrete Kirchhoff quadrilateral element is developed for static analysis of FG sandwich plates using Reddy’s 3rd-order theory. The model captures transverse shear stresses efficiently, validated through benchmark problems. Accurate results are obtained even for coarse mesh configurations.